32.9.6 problem Exercise 22.6, page 240

Internal problem ID [5980]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number : Exercise 22.6, page 240
Date solved : Monday, January 27, 2025 at 01:29:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=12 \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=12*exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\left (-2 \,{\mathrm e}^{3 x}-c_{2} {\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==12*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (2 e^{3 x}+c_2 e^x+c_1\right ) \]